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Vizi Z., Marciniak K., Przybylak R., Wójcik G.
Department of Climatology, Nicholas Copernicus University,
Danielewskiego 6, 87-100 Torun, Poland
Fax: (+48 56) 6223936, Tel: (+48 56) 6224305


For the investigation of climatic change or climatic variation in recent decades, it is mainly the homogenised temperature and precipitation series which are most needed. In Poland, the analysis of long time series of meteorological data is quite difficult. Firstly, there are only a few stations with long observations which due to historical reasons (mainly wars), are often not continuous. Secondly, it is very difficult to find documentation about the stations' history before World War II. Thirdly, those observations which are available are often not homogenous due to different observational systems and the relocation of stations.
At present, homogenised temperature series for the area of Poland are only available for a few stations located in the coastal region of the Baltic Sea (Mietus 1996, 1998), in central (Górski and Marciniak 1992; Lorenc 2000) and in southern Poland (Glowicki 1997, Trepinska 1997). One of our aims realised within a project supported by a grant from the Scientific Research Committee (grant no. 6 P04E 022 16) has been to check which series from Polish stations are and are not homogeneous. Non-homogenised series will be corrected using both the Standard Normal Homogeneity Test (Alexandersson 1986; Alexandersson and Moberg 1987) and the multiple regression method (Vincent 1990, 1998). We began our investigation by checking the quality and homogeneity of annual air temperature series from Bydgoszcz, which has the longest record in the Kujawsko-Pomorski region, dating from 1848. In addition, the station's history is well documented and the station itself well represents the climatic conditions in central Poland. The location of both this and other stations mentioned in this paper are shown in Fig. 1.
The main aim of this paper is to obtain homogeneity temperature series from Bydgoszcz using the above-mentioned methods.

Figure 1:
Spatial distribution of the stations used.
Triangle - the candidate station
Squares - stations used to fill up missing values
Circles - reference stations


The meteorological station in Bydgoszcz is located in the Notec-Warta ice-marginal valley ( =  53° 8' N, =  18° 0' E, h = 46 m a. s. l.)  by the Brda River. To the north and south of the city there are 70-100 m and 30-40 m elevations above the river level, respectively.
Regular meteorological observations began in Bydgoszcz on 1 January 1848 and have continued till now with two breaks during World War II (Hohendorf 1948). During the first 60 years the places of observations changed together with the addresses of observers (1854, 1887); from 1887 to 1907 the station was located at the local teacher's college.
In 1905 the Agricultural Institute (at present: Institute for Land Reclamation and Grassland Farming, Al. Ossolinskich 12) was founded in Bydgoszcz and a meteorological station was also organised there with the newest instruments available at that time. The observations were published in "Ergebnisse der meteorologishen Beobachtungen" until World War I.
From 1908 observations were made only at the Agricultural Institute. In 1930 the location of the station was changed from the park near the Institute to an open area 70 m away from the buildings. In September 1939, after the German invasion, the observations were interrupted until 1 January 1941. During the war, measurements were made only on workdays and, in addition, at non-standard times (usually at 8 a.m., 1 p.m. and 5 p.m.) when daylight permitted. For example, in winter the morning observations were made later and the evening ones earlier. For these reasons, the meteorological data from this period are almost unusable. Materials from recorded instruments, which could help to reconstruct the course of some elements, were destroyed during the war.
There was another meteorological station established before the war at Bydgoszcz airfield that worked during the occupation, but it was completely destroyed in 1945 together with all of the meteorological materials.
After the war meteorological observations began again in September 1945. In 1946 the location was changed to an open field. Since this time the station has been in operation continuously. In 1970 the method of the daily mean temperature calculation was changed and now it is calculated from 4 measurements instead of the former 3.
       Raw data series of annual air temperature from Bydgoszcz was obtained:
- until 1920 from Smosarski (1923), - 1921-1937 from meteorological yearbooks published by the State Meteorological Institute and the State Hydro-Meteorological Institute in Warsaw,
- 1938-1953 from the Institute for Land Reclamation and Grassland Farming,
- 1954-1968 from meteorological yearbooks published by the State Hydro-Meteorological Institute in Warsaw,
- 1969-1990 from the Institute for Land Reclamation and Grassland Farming.
Gaps in the series were filled on the basis of data from nearby stations (Torun and Poznan) using the method of constant differences. The complete series which was thus obtained for the period 1851-1990 was checked for inhomogeneities. As mentioned above two methods were used for this purpose. The first method, the Standard Normal Homogenity Test (SNHT), is very popular and well known, so there is no need to present it in more detail. The second, the multiple regression method, is less known and up till now was mainly used for Canadian stations. For this reason we present a brief account of it here. This method applies four models successively (Vincent 1998):

Model 1. Homogeneous series

where yi: the temperature at the candidate station at time i
xj,i: the temperature at station j at time i
n: the number of values in the time series
N: the total number of reference stations
ei: differences between the temperature values at the candidate
station and the fitted values.

The dependent variable is the temperature at the candidate station (yi) and the independent variables are the temperatures at the reference stations (xij). The parameters a, cj are calculated using the least square method. The residuals ei are analysed for autocorrelation. To determine the significance of autocorrelation in lag one the Durbin-Watson D statistic is calculated (Draper and Smith 1981; Neter et al. 1985):

The autocorrelation coefficient at lag k (Chatfield 1984) is:

If the autocorrelation in the residuals (rk) is significantly different from zero at several consecutive low lags then the series is probably inhomogeneous and other models are fitted to the data.

Model 2. Trend

A new variable is added to Model 1:

The parameter b shows the slope of the regression line.

Model 3. Shift

where b: the magnitude of the step
I = 0      for     i = 4,      ,k-1
I = 1      for     i = k,      ,n-3
k: the position of the change-point in time.

To determine the breakpoint, the model is used successively for different k values. The minimum of the obtained residual sum square series (RSS) indicates the most probable position of the breakpoint in time (Gullett et al. 1991; Vincent 1990). The variable I gives the change in the mean level and the parameter b the magnitude of the step.

Model 4. Trends before and after a break

where: I1 = 1    and      I2 = 0        for    i = 4,      ,k-1
I1 = 0    and      I2 = 1        for    i = k,...,n-3
k: the position of the change-point in time.

The minimum of the RSS determines the best fit, and the parameters b1 and b2 represents the slopes of the regression lines before and after the step, respectively. The magnitude of the step is:

m = (a1 + a2 + b2k) - (a1 + b1(k-1))

After the application of the models successively the autocorrelation in residuals is tested using the Durbin-Watson test and the correlogram. If a significant autocorrelation is found then the given model does not describe adequately the series and further analysis is necessary. In the case of significant autocorrelation after the application of Model 4, the series is divided into subseries at the estimated breakpoint and the subseries are tested again.


Although meteorological observations are available since 1848 for Bydgoszcz, we have chosen the period 1851-1990 for our homogeneity test due to the existing homogeneous reference series for this period. The selected reference stations were Gdansk and Hel (homogenised by Mietus 1998), Warsaw, as well as two stations outside Poland: Berlin and Prague. The data were taken from the following sources: Meteorologicka pozorovani w Praze-Klementinum 1976; Groveman and Landsberg 1979; Marciniak and Kozuchowski 1990; Mietus 1998. There are some more long temperature series from Polish or neighbouring countries' stations but we did not use them because they either have long breaks or the correlation with the Bydgoszcz series is too low. The correlation between the annual mean temperatures of the selected reference series and Bydgoszcz is shown in Table 1.

Table 1:
Correlation coefficients between the annual mean temperatures at Bydgoszcz and the reference stations for the period 1851-1990
Figure 2:
Differences in annual air temperature between Bydgoszcz and the selected reference series for the period 1851-1990.

Analysis of the graphical display of the candidate time series, or of those of the difference series, can give a subjective judgement about inhomogeneities. Figure 2 shows the difference series between Bydgoszcz and the selected reference stations. It can be clearly seen that at the end of the time series of the 1970s there is a shift in the analysed station's data. The differences in the data at the beginning of the time series also indicate some inhomogeneities.
In the next step we have applied the SNHT using the above-mentioned reference stations. Figure 3 presents the courses of the annual air temperature, Q-series and T-series before and after homogenisation. The detected change points are 1886 (Tmax = 22.3; shift: 0.3°C) and 1970 (Tmax = 57.7; shift: 0.5°C).

Figure 3:
Annual temperature, Q-series, and T-series (T90 critical level) for Bydgoszcz before (left panel) and after (right panel) homogenisation for the period 1851-1990.

We have also applied the multiple regression method to the same temperature series. Firstly, Model 1 was fitted to the data. The obtained residuals are presented in Figure 4. This clearly indicates inhomogeneities at the beginning and end of the series. After the application of the other models, we have obtained the following shifts: 1886 (0.4°C), 1939 (0.1°C) and 1970 (0.5°C). The method has been tested on simulated series (Vincent 1998) and was found that it frequently identifies steps over 0.5°C, but steps of 0.25°C and lower are infrequently identified. Therefore steps below 0.25°C are usually not corrected.

Figure 4:
Residuals and autocorrelation of the residuals obtained after fitting Model 1 before (left panel) and after (right panel) adjustment of the mean annual temperature data at Bydgoszcz for the period 1851-1990.

The most probable reason for the homogeneity detected in 1886 is the relocation of the station mentioned earlier. The second large inhomogeneity in 1970 is connected with the changes of observational hours (from 7 a.m., 1 p.m. and 9 p.m. LT to 1 a.m., 7 a.m., 1 p.m. and 7 p.m. CET) and the calculation of the daily mean temperatures. We did not take into account the small shift detected in 1939, but we suppose that it can be related to the errors in the process of filling the missing data.


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